The chapter studies nine long-known extant Chinese mathematical texts, and three recently excavated texts, all composed prior to the beginning of the Sui 隋 dynasty (581–618 ce). Most of these were compiled for use as school texts. They include problems on fractions, on proportions and extraction of square and cube roots, on simultaneous linear equations and computations of areas and volumes. Among the more advanced techniques deployed in these texts are computing the area of a circle, that is, obtaining certain approximate values of π; computing the volume of a pyramid; and computing the volume of a sphere.
The chapter studies ancient Chinese astronomy, which focused on computing and predicting the movements of the heavens (天 tian), the sun, moon, stars, and asterisms, which was the duty of the rulers, in order that the people be well-regulated. Heavenly bodies were allocated to terrestrial zones, especially 28 constellations roughly along the equator or the ecliptic, the seven stars of the Big Dipper (regarded as the carriage of heaven), and the five planets. Unusual celestial phenomena were recorded, such as solar eclipses, comets, and meteorites. The 盖天 gai tian theory (celestial dome theory), the 浑天 hun tian Theory (celestial sphere theory) and the 宣夜 xuan ye theory (infinite empty space theory) were the three primary theories of the structure of the heaven and the earth, in the Han dynasty (202 bce—220 ce). The earliest extant Chinese star catalogue of the whole sky was composed in the 1st century bce, and the definitive constellation system of 283 constellations, 1464 or 1465 stars was composed in the 3rd century ce.
The chapter explores Mesopotamian astrology and astronomy, which were not distinct as pseudo-science is from science, and were together a major part of cuneiform intellectual culture. The writings consist of scholarly compendia, observational records, and predictive ephemerides, mostly produced after ca700 bce, at the court in Assyria, and later, in the major temples of Babylonian cities. Heavenly phenomena (astral, planetary, and lunar) were objects of study both as signs of future events and as phenomena in their own right. The systematic study and recording of astral phenomena as signs began in the Old Babylonian period (2000–1600 bce), and continued well after the conquest by Alexander. Babylonian astronomy used mathematical models (based on numerical sequences) to calculate periodic phenomena. The astral sciences, including celestial and natal divination, that is, omens and horoscopes, were parts of a scholarly discipline sustained over two millennia by cuneiform scribes in both Assyria and Babylonia.
In its original Babylonian and Egyptian contexts, astrology was the interpretation of celestial signs and omens sent by the gods as warnings to rulers and the elite. Roman fondness for Stoicism fertilized the growth of astrology in the Greco-Roman world, which developed into a natural science, fully integrated with the prevailing cosmology. Astrology became popularized, and anyone who could afford some level of the service knew basic features of his natal chart. The chapter explains the various forms and purposes of judicial or divinatory astrology: “mundane” (heavenly effects on regions), “genethlialogical” (heavenly effects on a life from its birth or conception), “horary” (heavenly effects on the present moment), and “catarchic” (heavenly effects on the future). The chapter also provides an historical sketch of classical astrology, from Babylonian origins through the major surviving handbooks, and an elaborated ancient example of a natal chart (of the emperor Hadrian), its methods, and interpretation.
This chapter studies Egyptian astronomy based on the very few surviving texts. The Egyptian calendar was purely solar, unlike most ancient calendars. The oldest astronomical monuments from Egypt are the star clocks, mainly on the interior of coffin lids from the Eleventh and Twelfth Dynasties. They divide the year into 36 ten-day intervals (decades), each with 12 stars, to mark the hours of the night for religious purposes. The major text of Egyptian astronomy is the Book of Nut, the sky goddess, which describes the behavior of the sun, moon, and especially fixed stars, as well as shadow clocks and water clocks. The Egyptian constellations were fundamentally different from ours (based on Mesopotamian and Greek myths), with Osiris (our Orion), Seth (our Big Dipper), and Sirius playing a prominent role, plus the Ship, the Sheep, and the Two Tortoises. Late Egyptian astronomy borrows some techniques from Mesopotamian astronomy. In the Greco-Roman period, Egyptian astronomy borrows elements from Greco-Roman astronomy.
The chapter shows how the texts of early Byzantine alchemy transformed the alchemical tradition. This period is characterized by a generation of “commentators” tied to the Neoplatonic milieu. Their writings, designed primarily to clarify the ideas of the previous generations, represent the most advanced stage of ancient alchemical theory. In the fifth century, authors external to alchemy explicitly speak of alchemy as a contemporary practice to produce gold from other metals. Around the seventh century, the corpus of alchemical texts began to be assembled as an anthology of extracts. The object of the research was agents of transformations of matter. The cause of the transformation is an active principle that acts by dissolution: “divine water” (or sulfur water), mercury, “chrysocolla” (gold solder), or raw sulfur. Mercury is at once the dyeing agent and the prime metallic matter, understood as the common substrate of the transformations and the principle of liquidity.
The chapter maps out the various forms and modes of Greek geographical writing and thinking in the early Byzantine period. Geography in Byzantium means transmission of the ancient Greeks’ knowledge and the handling of this material by certain scholars, via copying manuscripts, making extracts from the old writings, or writing separate commentaries. The two ancient writers that most influenced geographical ideas of the Byzantines were Strabo and Ptolemy. Besides geographical treatises, such as those by Marcian, Protagoras, Hierocles, and Stephen, many historical works contained extensive geographical excursuses (for example, Philostorgius), and reports of ambassadors often included a geographical description of the land(s) they visited. Christians of the school of Antioch tended to deny the spherical earth theory (Theophilus of Antioch, Diodorus of Tarsus, Theodorus of Mopsuestia, Kosmas of Alexandria). Itineraries and traveler’s accounts provide a glimpse of how people traveled. The Peutinger map displays the Roman roads around 435 ce.
The contribution of the Byzantine medical encyclopedists (ca 370 ce–ca 650 ce) to the preservation of medical knowledge still awaits its full scholarly assessment. This chapter highlights the achievements of Oribasius of Pergamum, Aëtius of Amida, Alexander of Tralleis, and Paul of Aegina. In the shadow of Galen’s legacy, these writers preserve, organize, and explicate the diverse body of medical knowledge, available to them. Relying on Galen but also on medical writers from the sixth century bce onwards, Oribasius composes his Compilations as a comprehensive source of medical authority. Aëtius produces a collection of 16 books covering the full medical spectrum from pharmacology to diagnostics to pathology. To it, Alexander adds a collection of 12 books, entitled Therapeutics, with corollary treatises On Fevers and On Intestinal Worms. Paul compiles the Epitome of Medicine, featuring all medical branches.
The chapter discusses ancient Greek dietetic theory and practice; for Greek physicians and patients, diet was one of the primary means of medical intervention. Diet was treated along with exercise, as well as sleep, massage, drugs, and sex. The many authors of the Hippocratic differed about diet, and Galen favors his own advice. We have mere scraps from Hellenistic authors such as Diocles of Carystus, Archestratus, Mnesitheus of Athens, Diphilus of Siphnos, and Phylotimus. The late antique Latin cookbook “Apicius” (likely named for the first-century ce gourmand), promotes a style of cookery that survived into the mediaeval world: blending numerous seasonings and the characteristic balance between sweet and sour, still redolent in the traditional agrodolce sauces of Italian cuisine. Theories of diet and digestion varied enormously as well, Hippocrates claiming concoction, Erasistratus thinking of mechanical grinding and dispersion, and others deciding upon distribution, the more dominant theory in late antiquity.
This chapter re-examines the historiography of Greco-Egyptian alchemy. The author challenges the representation of alchemy as a superficial amalgam (or “syncretism”) of Greek philosophical theories. He argues for an indigenous Egyptian development of the art, rooted distantly in the artisanal traditions of the temples, and stresses the originality of alchemical matter theory, which drew creatively on Greek philosophical (especially Aristotelian) concepts. The alchemists were also innovative technicians, developing new methods and apparatus in pursuit of the goal of transmutation. These theoretical and technical innovations contradict the commonplace image of alchemy as an irrational pseudo-science. The esotericism of alchemy, far from undermining its rational development, served to stimulate research, since the secrets of the ancient masters could only be decoded in the light of laboratory experience. Alchemy does not provide evidence for a (supposed) decline into mystical obscurantism in the late ancient world.